PSEUDODIFFERENTIAL-OPERATORS ON COMPACT MANIFOLDS WITH LIPSCHITZ BOUNDARY

Pseudodifferential operators with non-smooth symbols on a manifold M w ith LIPSCHITZ boundary are considered. Theorems about order reduction and localization of such operators in BESSEL potential H(p)s(M) and HO LDER-ZYGMUND Z(p)alpha(R(n)) spaces are proved. A pseudodifferential o perator A with locally sectorial matrix symbol is proved to be FREDHOL M in the space H-2s (M) and Ind A = 0 where s depends on A. Applicatio n to a boundary value problem for an elastic body with crack is discus sed in conclusion.